Chameleon-photon mixing in a primordial magnetic field

The existence of a sizable, O(10-10-10-9 G), cosmological magnetic field in the early Universe has been postulated as a necessary step in certain formation scenarios for the large-scale O(μG) magnetic fields found in galaxies and galaxy clusters. If this field exists then it may induce significant mixing between photons and axion-like particles (ALPs) in the early Universe. The resonant conversion of photons into ALPs in a primordial magnetic field has been studied elsewhere by Mirizzi, Redondo and Sigl (2009). Here we consider the nonresonant mixing between photons and scalar ALPs with masses much less than the plasma frequency along the path, with specific reference to the chameleon scalar field model. The mixing would alter the intensity and polarization state of the cosmic microwave background (CMB) radiation. We find that the average modification to the CMB polarization modes is negligible. However the average modification to the CMB intensity spectrum is more significant and we compare this to high-precision measurements of the CMB monopole made by the far infrared absolute spectrophotometer on board the COBE satellite. The resulting 95% confidence limit on the scalar-photon conversion probability in the primordial field (at 100 GHz) is Pγ↔φ<2.6x10-2. This corresponds to a degenerate constraint on the photon-scalar coupling strength, geff, and the magnitude of the primordial magnetic field. Taking the upper bound on the strength of the primordial magnetic field derived from the CMB power spectra, Bλ≤5.0x10-9 G, this would imply an upper bound on the photon-scalar coupling strength in the range geff < or approx. 7.14x10-13 GeV-1 to geff < or approx. 9.20x10-14 GeV-1, depending on the power spectrum of the primordial magnetic field.